This is a first competitive renewal of a Program Project Grant with the goal of developing experimental and computational tools of cryo-electron microscopy in the context of a widening range of biological applications. Atomic resolution pictures of complex assemblies are the ultimate objectives. The renewal has three central themes. The first is a focus on membrane proteins and membrane-associated assemblies. We will expand work from the first grant period on 2-D membrane protein crystals, on clathrin-coated vesicles, and on single particle analysis as applied to membrane proteins. The second theme is development of maximum likelihood methods in single-particle reconstructions, with the goal of extending our ability to obtain molecular structural information from conformationally heterogeneous specimens. The results of the previous grant period demonstrate that x-ray crystallography and cryo-EM form a smooth continuum of methods that indeed can achieve atomic resolution for a great variety of homogeneous samples. The goal is now to improve the robustness of single-particle reconstruction algoirthms and to deal with conformationally heterogeneous single particles. Cryo-electron tomography of macromolecular complexes will also have a role in bridging between lower resolution analyses of the assemblies and high-resolution analyses of their substructures. The third theme is precisely the application of these methods to transient, multi-state assemblies, such as spliceosomes and kinetochore substructures.